Mehdi Lhommeau

Interval analysis and dioid: application to robust controller design for timed event graphs

This paper deals with feedback controller synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a robust controller set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each controller is computed in order to guarantee that the closed-loop system behavior is greater than the lower bound of a reference model set and is lower than the upper bound of this set. The synthesis presented here is mainly based on dioid, interval analysis and residuation theory.

Observer Design for

This technical note deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation of the input and of the output is used to compute the estimated state. The observer design is based on the residuation theory which is suitable to deal with linear mapping inversion in idempotent semiring.

(\max, +)

Abstract This paper presents a design method for a state observer of max-plus linear systems based on the observation of the input and the output, by assuming the knowledge of the system matrices. The observer design is done in an analogous way to the observer method for classical linear system. The paper will be concluded by an illustration.

Linear Systems

This paper deals with solution of inequality A x b, where A; x and b are interval matrices with entries dened over idempotent semiring. It deals also with the computation of a pair of intervals, (x; y) which satises the equation

OBSERVER DESIGN FOR MAX-PLUS-LINEAR SYSTEMS

This paper deals with control of (max,+)-linear systems when a disturbance acts on system state. In a first part we synthesize the greatest control which allows to match the disturbance action. Then, we look for an output feedback which makes the disturbance matching. Formally, this problem is very close to the disturbance decoupling problem for continuous linear systems.

Interval systems over idempotent semiring

This paper deals with robust open-loop control synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a greatest interval of control included in the robust control set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each control is computed in order to guarantee that the controlled system behavior is greater than the lower bound of a desired output reference set and is lower than the upper bound of this set. The synthesis presented here is mainly based on dioid, interval analysis and residuation theory.

Optimal Control for (max,+)-linear Systems in the Presence of Disturbances

This paper deals with control of timed event graphs (TEG) when a disturbance acts on transitions. We synthesize the greatest feedback controller which allows to match the disturbance action. Formally, this problem is very close of the classical problem of disturbance decoupling for linear systems.

Interval Analysis in Dioid: Application to Robust Open-Loop Control for Timed Event Graphs

The max-plus linear systems have been studied for almost three decades, however, a well-established system theory on such specific systems is still an on-going research. The geometric control theory in particular was proposed as the future direction for max-plus linear systems by Cohen et al. This paper reports upon recent investigations on the disturbance decoupling problem for max-plus linear systems, which is the standard geometric control problem originated by W. M. Wonham. Different concepts of the disturbance decoupling problem are introduced, as well as the corresponding solvability conditions and controller synthesis procedures. The main results can be used in manufacturing systems, queueing networks, and power system networks for fault detection and system breakdown prevention.

About disturbance decoupling of timed event graphs in dioids

This talk will present the Scilab toolbox for Network Calculus computation. It was developed thanks to the INRIA ARC COINC project (COmputational Issue in Network Calculus see http://perso.bretagne.ens-cachan.fr/~bouillar/coinc/spip.php?rubrique1). This software library deals with the computation of ultimate pseudo-periodic functions. They are very useful to compute performance evaluation in network (e.g. Network Calculus) or in embedded system (Real Time Calculus).

Towards geometric control of max-plus linear systems with applications to manufacturing systems

This paper presents the new investigations on the disturbance decoupling problem (DDP) for the geometric control of max-plus linear systems. The classical DDP concept in the geometric control theory means that the controlled outputs will not be changed by any disturbances. In practical manufacturing systems, solving for the DDP would require further delays on the output parts than the existing delays caused by the system breakdown. The new proposed modified disturbance decoupling problem (MDDP) in this paper ensures that the controlled output signals will not be delayed more than the existing delays caused by the disturbances in order to achieve the just-in-time optimal control. Furthermore, this paper presents the integration of output feedback and open-loop control strategies to solve for the MDDP, as well as for the DDP. If these controls can only solve for the MDDP, but not for the DDP, an evaluation principle is established to compare the distance between two output signals generated by controls solving for the MDDP and DDP, respectively. This distance can be interpreted as the number of tokens or firings that are needed in order for the controls to solve for the DDP. Moreover, another alternative approach is finding a new disturbance mapping in order to guarantee the solvability of the DDP by the same optimal control for the MDDP. The main results of this paper are illustrated by using a timed event graph model of a high throughput screening system in drug discovery.